Systems and methods for determining the N-best strings

ABSTRACT

Systems and methods for identifying the N-best strings of a weighted automaton. A potential for each state of an input automaton to a set of destination states of the input automaton is first determined. Then, the N-best paths are found in the result of an on-the-fly determinization of the input automaton. Only the portion of the input automaton needed to identify the N-best paths is determinized. As the input automaton is determinized, a potential for each new state of the partially determinized automaton is determined and is used in identifying the N-best paths of the determinized automaton, which correspond exactly to the N-best strings of the input automaton.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/301,098, filed Nov. 21, 2002, which is currently allowed and claimspriority to U.S. Provisional Patent Application Ser. No. 60/369,109,filed on Mar. 29, 2002, both of which are incorporated herein byreference in their entirety.

BACKGROUND OF THE INVENTION

1. The Field of the Invention

The present invention relates to identifying a ranked list of uniquehypotheses and more specifically to determining the N-best strings of anautomaton. More particularly, the present invention relates to systemsand methods for determining the N-best distinct strings of a weightedautomaton through partial determinization of the weighted automaton.

2. The Relevant Technology

A speech recognition system is an example of a computing system thatconverts real world non-digital type input data into computer-usabledigital data and that converts computer digital data into real-worldoutput data. A speech recognition system receives speech from a varietyof different sources, such as over the telephone, through a microphoneor through another type of transducer. The transducer converts thespeech into analog signals, which are then converted to a digital formby the speech recognition system. From the digital speech data, thespeech recognition system generates a hypothesis of the words orsentences that were contained in the speech. Unfortunately, speechrecognition systems are not always successful at recognizing speech.

In order to improve the likelihood of correctly recognizing the speech,speech recognition systems generally try to make a best guess orhypothesis using statistical probabilities. In fact, speech recognitionsystems often generate more than one hypothesis of the words that makeup the speech. In one example, the various hypotheses are arranged in alattice structure such as a weighted automaton, where the weight of thevarious transitions in the automaton correlate to probabilities.

The weighted automaton or graph of a particular utterance thusrepresents the alternative hypotheses that are considered by the speechrecognition system. A particular hypothesis or string in the weightedautomaton can be formed by concatenating the labels of selectedtransitions that form a complete path in the weighted automaton (i.e. apath from an initial state to one of the final states). The path in theautomaton with the lowest weight (or cost) typically corresponds to thebest hypothesis. By identifying more than one path, some speechrecognition systems are more likely to identify the correct string thatcorresponds to the received speech. Thus, it is often desirable todetermine not just the string labeling a path of the automaton with thelowest total cost, but it is desirable to identify the N-best distinctstrings of the automaton.

The advantage of considering more than one hypothesis (or string) isthat the correct hypothesis or string has a better chance of beingdiscovered. After the N-best hypotheses or paths have been identified,current speech recognition systems reference an information source, suchas a language model or a precise grammar, to re-rank the N-besthypotheses. Alternatively, speech recognition systems may employ are-scoring methodology that uses a simple acoustic and grammar model toproduce an N-best list and then to reevaluate the alternative hypothesesusing a more sophisticated model.

One of the primary problems encountered in evaluating the N-besthypotheses is that the same string is often present multiple times. Inother words, the automaton or word lattice often contains several pathsthat are labeled with the same sequence. When the N-best paths of aparticular automaton are identified, the same label sequence may bepresent multiple times. For this reason, current N-best path methodsfirst determine the k (k>>N) shortest paths. After the k shortest pathshave been identified, the system is required to perform the difficultand computationally expensive task of removing redundant paths in orderto identify the N-best distinct strings. Thus, a large number ofhypotheses are generated and compared in order to identify and discardthe redundant hypotheses. Further, if k is chosen too small, the N-bestdistinct strings will not be identified, but rather some number lessthan N.

The problem of identifying the N-best distinct strings, when compared toidentifying the N-best paths of a weighted automaton, is not limited tospeech recognition. Other systems that use statistical hypothesizing orlattice structures that contain multiple paths, such as speechsynthesis, computational biology, optical character recognition, machinetranslation, and text parsing tasks, also struggle with the problem ofidentifying the N-best distinct strings.

BRIEF SUMMARY OF THE INVENTION

These and other limitations are overcome by the present invention, whichrelates to systems and methods for identifying the N-best strings of aweighted automaton. One advantage of the present invention is thatredundant paths or hypotheses are removed before, rather than after, theN-best strings are found. This avoids the problematic enumeration ofredundant paths and eliminates the need to sort through the N-best pathsto identify the N-best distinct strings.

Determining the N-best strings begins, in one embodiment, by determiningthe potential of each state of an input automaton. The potentialrepresents a distance or cost from a particular state to the set of endstates. Then, the N-best paths are found in the result of an on-the-flyweighted determinization of the input automaton. Only the portion of theinput automaton needed to identify the N-best distinct strings isdeterminized.

Weighted determinization is a generalization of subset construction tocreate an output automaton such that the states of the output automatonor the determinized automaton correspond to weighted subsets of pairs,where each pair contains a state of the input automaton and a remainderweight. Transitions that interconnect the states are created and given alabel and assigned a weight. The destination states of the createdtransitions also correspond to weighted subsets. Because the computationof the transition(s) leaving a state only depends on the remainderweights of the subsets of that state and on the input automaton, it isindependent of previous subsets visited or constructed. Thus, the onlyportion of the input automaton that is determinized is the portionneeded to identify the N-best strings. The potential or shortestdistance information is propagated to the result of determinization.

An N-shortest path method that utilizes the potential propagated to theresult of determinization can be used to find the N-best paths of thedeterminized automaton, which correspond with the N-best distinctstrings of the input automaton. Advantageously, the determinizedautomaton does not need to be entirely expanded and/or constructed.

Additional features and advantages of the invention will be set forth inthe description which follows and in part will be obvious from thedescription, or may be learned by the practice of the invention. Thefeatures and advantages of the invention may be realized and obtained bymeans of the instruments and combinations particularly pointed out inthe appended claims. These and other features of the present inventionwill become more fully apparent from the following description andappended claims, or may be learned by the practice of the invention asset forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the manner in which the advantages and features of theinvention are obtained, a more particular description of the inventionbriefly described above will be rendered by reference to specificembodiments thereof which are illustrated in the appended drawings.Understanding that these drawings depict only typical embodiments of theinvention and are not therefore to be considered limiting of its scope,the invention will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 illustrates a weighted automaton that has not been determinized;

FIG. 2 illustrates a determinized automaton;

FIG. 3 illustrates a method for finding the N-best distinct strings ofan input automaton;

FIG. 4 illustrates a state creation process;

FIG. 5 illustrates an exemplary N-best paths method used to identify theN-best distinct strings of an input automaton; and

FIG. 6 illustrates the contents of a queue S for a specific example atvarious times during an N-best path algorithm.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Weighted directed graphs such as automata are used in a variety ofdifferent technologies, such as speech recognition, speech analysis,optical character recognition, text parsing, machine translation, andthe like. A weighted automaton may represent multiple hypotheses of aprobabilistic process such as those set forth above. The presentinvention relates to identifying or determining the N-best distinctstrings of the automata and is applicable in these and other areas.

One advantage of the present invention is that the redundant paths areremoved prior to determining the N-best paths. Because the redundantpaths are removed prior to the N-best search, the N-best pathscorrespond to the N-best distinct strings. The redundant paths areremoved in one embodiment by determinizing the weighted automatonon-the-fly until the N-best strings are identified. Because theredundant paths have already been removed by the partial determinizationof the weighted automaton, the N-best path process identifies the N-beststrings and the potentially exponential enumeration of redundant pathsis avoided. Another advantage of the present invention is thatdetermining the N-best strings does not require complete determinizationof the weighted automaton. Only the portion of the automaton visitedduring the N-best search is determinized. Alternatively, only theportion of the determinized automaton visited during the N-best searchis expanded.

Weighted automata are weighted directed graphs in which each edge ortransition has a label and a weight. Weighted automata are useful inmany contexts as previously described. While the present invention isdescribed in terms of speech recognition, one of skill in the artrecognizes the applicability of the present invention to other systemsusing weighted automata.

FIG. 1 illustrates an exemplary weighted automata that has beengenerated, in this example, by a speech recognition system. Theautomaton 100 includes a beginning state 0, a final state 3 andintermediary states 1 and 2. The states are connected by transitions andeach transition has a label and a weight. The label, in the case of aphoneme or word lattice, is usually a phoneme or a word respectively,although the label can represent any type or bit of information. Theweight of a transition is often interpreted as the negative log ofprobabilities, but may correspond to some other measured quantity. Theweight of a particular path in the automaton 100 is determined bysumming the weights of the transitions in the particular path. In thecase of a word automaton, a sentence can be determined by concatenatingthe labels for each path in the automaton 100.

More specifically in this example, the transitions 101 and 102 connectstate 0 with state 1. The transitions 103, 104, 105, and 106 connectstate 0 with state 2. The transitions 107 and 108 connect state 1 withstate 3, and the transitions 109 and 110 connect state 2 with state 3.Each transition has a label and a weight. For example, the label 111 ofthe transition 101 is “a” and the weight 112 of the transition 101 is0.1. The other transitions are similarly labeled.

An automaton is deterministic if it has a unique initial state and if notwo transitions leaving the same state share the same input label. Theautomaton 100 is therefore not deterministic because some of thetransitions leaving a particular state have the same label. In FIG. 1,for example, the transitions 101, 103, and 104 all leave state 0 andeach transition has the same label “a”. The automaton 100, however, canbe determinized.

More generally, an automaton A can be weighted over the semiring (R∪{−∞,+∞}, min, +, ∞, 0). Usually, the automaton is generally weighted overthe semiring (R₊∪{∞}, min, +, ∞, 0) also known as the tropical semiring.This example uses the weights along the tropical semiring A=(Σ, Q, E, iF, λ,=p) that are given by an alphabet or label set Σ, a finite set ofstates Q, a finite set of transitions E ⊂Qx Σ(R₊∪{∞}) x, an initialstate iεQ, a set of final states F⊂Q, an initial weight λ and a finalweight function p.

A transition e=(p[e], l[e], w[e], n[e])ε E can be represented by an arcfrom the source or previous state p[e] to the destination or next staten[e], with the label l[e] and weight w[e]. A path in A is a sequence ofconsecutive transitions e₁ . . . e_(n) with n[e_(i)]=p[e_(i+1)], i=1, .. . , n−1. Transitions labeled with the empty symbol ε consume no input.Denoted are P(R, R′), the set of paths from a subset of states R⊂Q toanother subset R′⊂Q. A successful path πe₁ . . . e_(n) is a path fromthe initial state i to a final state fεF. The previous state and nextstate for path π is the previous state of its initial transition and thenext state of its final transition, respectively:p[π]=p[e ₁ ],n[π]=n[e _(n)]  (1)The label of the path π is the string obtained by concatenating thelabels of its constituent transitions:l[π]=l[e ₁ ] . . . l[e _(n)]  (2)The weight associated to π is the sum of the initial weight (if p[π]=i),the weights of its constituent transitions:w[π]=w[e ₁ ]+ . . . +w[e _(n)]  (3)and the final weight p[n[π]] if the state reached by π is final. Asymbol sequence x is accepted by A if there exists a successful path πlabeled with x: l[π]=x. The weight associated by A to the sequence x isthen the minimum of the weights of all the successful paths π labeledwith x.

Weighted determinization is a generalization of subset construction. Inweighted determinization, a deterministic output automaton is generatedfrom an input automaton. The states of the output automaton correspondto weighted subsets {(q_(o),w_(o)), . . . , (q_(n), w_(n))} where eachq_(i)εQ is a state of the input automaton, and w_(i) a remainder weight.Weighted determinization begins with the subset reduced to {(i,0)} andproceeds by creating a transition labeled with aεΣ and weight w leaving{q_(o),w_(o)), . . . , (q_(n), w_(n))} if there exists at least onestate q_(i) admitting an outgoing transition labeled with a, w beingdefined byw=min{w _(i) +w[e]:eεE[q _(i) ],l[e]=a}.  (4)

The destination state of that transition corresponds to the subsetcontaining the pairs (q′, w′) with q′ε{n[e]:p[e]=q_(i), l[e]=a} and theremainder weightw′=min[w _(i) +w[e]−w:n[e]−w:n[e]=q′}.  (5)

A state is final if it corresponds to a weighted subset S containing apair (q, w) where q is a final state (qεF) and in that case its finalweight is:w=min{w+p[q]:(q, w)εS,qεF}.  (6)

FIG. 2 illustrates a determinized automaton 200, which is the automaton100 after it has been determinized. The determinized automaton 200includes a start state 0′, a final state 3′, and intermediate states 1′and 2′. The weighted automaton 200 is deterministic because no twotransitions leaving a particular state share the same label.

The following discussion illustrates the determinization of theautomaton 100 in FIG. 1 into the automaton 200 of FIG. 2 using thedeterminization process briefly described previously. The transitions101, 103, and 104 all leave state 0 and all have the label a. Atransition 201 is thus created in the determinized automaton 200 withthe label a. The weight assigned to the transition 201 is determined as:w=min {w_(i)+w[e]:eεE[q_(i)], l[e]=a}. Applying this definition to thetransitions 101, 103, and 104 and taking the minimum results in a weightw of 0.1, which is assigned to the transition 201. Because thetransitions 101, 103, and 104 have two destination states (state 1 andstate 2) in the automaton 100, the destination state 1′ of thedeterminized automaton 200 for the transition 201 labeled a correspondsto the subsets containing the pairs (q′, w′) with q′ ε{n[e]:p[e]=q_(i),1[e]=a} and the remainder weight w′=min[w_(i)+w[e]−w:n[e]−w:n[e]=q′}.More specifically, the subset pairs of state 1′ are the pairs {(1,0),(2,0.1)}.

Using a similar procedure for the transitions 102, 105, and 106 resultsin the transition 202, which is labeled b and has a weight of 0.1. Thesubset of pairs that correspond to state 2′ are {(1,0.2),(2,0)}. Thetransitions 203, 204, 205, and 206 are similarly determined. Weighteddeterminization is more fully described in U.S. Pat. No. 6,243,679 toMohri et al., which is hereby incorporated by reference.

The computation of the transitions leaving a subset S only depends onthe states and remainder weights of that subset and on the inputautomaton. The computation is independent of the previous subsetsvisited or constructed and subsequent states that may need to be formed.This is useful because the determinization of the input automaton can belimited to the part of the input automaton that is needed. In otherwords, the input automaton can be partially determinized or determinizedon-the-fly.

FIG. 3 illustrates an exemplary method for finding the N-best distinctstrings of an input automaton. As previously indicated, redundant pathsare removed by the present invention such that the N-best paths of theresult of determinization correspond to the N-best strings of the inputautomaton. More specifically with reference to FIGS. 1 and 2, the N-bestpaths of the automaton 200 correspond to the N-best distinct strings ofthe automaton 100.

Identifying the N-best strings begins with determining the shortestdistance or potential of each state in an input automaton to a set offinal states (302) of the input automaton. Then, the N-best paths in theresult of an on-the-fly determinization of the input automaton (304) arefound. As previously stated, the N-best paths found in the result of theon-the-fly determinization correspond to the N-best distinct strings.

In the input automaton, the shortest distance or potential of each stateto a set of final states is given by:φ[q]=min{w[π]+p[f]:πεP(q,f),fεF}.  (7)The potentials or distances φ[q] can be directly computed by running ashortest-paths process from the final states F using the reverse of thedigraph. In the case where the automaton contains no negative weights,this can be computed for example using Dijkstra's algorithm in timeO(|E|log|Q| using classical heaps, or in time O(|E|+|Q|log|Q| ifFibonacci heaps are used.

As previously stated, the present invention does not require thecomplete determinization of the input automaton. However, theshortest-distance information of the input automaton is typicallypropagated to the result of the on-the-fly determinization. Further, theon-the-fly determinized result may be stored for future reference. Thepotential of each state in the partially determinized automaton isrepresented by Φ(q′) and is defined as follows:Φ[q′]=min{w_(i) =φ[q _(i)]:0≦i≦n},  (8)where q′ corresponds to the subset {(q_(o),w_(o)), . . . , (q_(n),w_(n))}. The potential Φ[q′] can be directly computed from eachconstructed subset. The potential Φ[q′] or determinized potential can beused to determine the shortest distance from each state to a set ofdeterminized final states within the partially determinized automaton.Thus, the determinized potential can be used in shortest pathalgorithms. The determinized potential is valid even though thedeterminized automaton is only partially determinized in one embodiment.

When an automaton is determinized on-the-fly during the N-best search,it is necessary to create new states in the result of on-the-flydeterminization as illustrated in FIG. 4. After a new state is created(402), the transition between the previous state and the new state iscreated (404) as described previously. Next, the pairs of the subsetthat correspond to the newly created state are determined (406).Finally, the potential for the new state is computed (408). The pairsincluded in the subset of a determinized state are used in the N-bestpath method described below.

In general, any shortest-path algorithm taking advantage of thedeterminized potential can be used to find the N-best paths of thepartially determinized automaton, which are exactly labeled with theN-best strings of the input automaton. The following pseudocode is anexample of an N-shortest paths algorithm that takes advantage of thedeterminized potential. This example assumes that the determinizedautomaton only contains a single final state. This does not affect thegenerality of the ability to identify the N-best strings because anautomaton can always be created by introducing a single final state f towhich all previously final states are connected by ε-transitions. Notethat the states of the determinized automaton are created only asrequired. The pseudocode is as follows:

 1 for p ← 1 to [Q′] do r[p] ← 0  2 π[i′, 0)] ← NIL  3 S ← {(i′, 0)}  4while S ≠ Ø  5 do (p, c) ← head(S); DEQUEUE(S)  6 r[p] ← r[p] + 1  7 if(r[p] = n and p ∈ F) then exit  8 if r[p] ≦ n  9 then for each e ∈ E[p]10 do c′ ←c + w[e] 11 π [n[e], c′)] ←(p, c) 12 ENQUEUE (S, (n [e], c′))

Consider pairs (p, c) of a state pεQ′ and a cost c, where Q′ is theautomaton representing the result of determinization. The process uses apriority queue S containing the set of pairs (p, c) to examine next. Thequeue's ordering is based on the determinized potential Φ and defined by(p,c)<(p′,c)

(c+Φ[p]<c′+Φ[p′])  (9)An attribute r[p], for each state p, gives at any time during theexecution of the process the number of times a pair (p, c) with state phas been extracted from S. The attribute r[p] is initiated to 0 (line 1)and incremented after each extraction from S (line 6).

Paths are defined by maintaining a predecessor for each pair (p, c)which will constitute a node of the path. The predecessor of the firstpair considered (i′, 0) is set to NIL at the beginning of each path(line 2). The priority queue S is initiated to the pair containing theinitial state i′ of Q′ and the cost 0.

Each time through the loop of lines 4-12, a pair (p, c) is extractedfrom S (line 5). For each outgoing transition e of p, a new pair(n[e]c′) made of the destination state of e and the cost obtained bytaking the sum of c and the weight of e is created (lines 9-10). Thepredecessor of (n[e], c′) is defined to be (p, c) and the new pair isinserted in S (lines 11-12).

The process terminates when the N-shortest paths have been found. Forexample, the process terminates when the final state of B has beenextracted from S N times (lines 7). Since at most N-shortest paths maygo through any state p, the search can be limited to at most Nextractions of any state p (line 8). By construction, in each pair (p,c), c corresponds to the cost of a path from the initial state i′ to pand c+Φ(p) to the cost of that path when completed with a shortest pathfrom p to F. The determinized potential is thus used in the result ofdeterminization. The partially determinized automaton is createdon-the-fly as the search for the N-best paths is performed on thepartially determinized automaton.

Because the pairs are prioritized within the queue, the order in whichnew states of the determinized automaton are created is effectivelydetermined by the N-best search. In other words, weighteddeterminization as described herein depends on the subset of pairs thatcorrespond to a particular state of the determinized automaton and onthe potential that is propagated to the determinized automaton. Thus,the N-best search utilizes the propagated potential and the subset ofstate pairs to determine how the input or original automaton isdeterminized on-the-fly.

The following example illustrates on-the-fly determinization withreference to FIGS. 1, 2, 5, and 6. In the present example, thedeterminized automaton 200 is constructed as the N-best strings arerealized as shown in FIG. 5. Identifying the N-best strings of aweighted automaton 100 begins by creation of an initial state that isadded to a determinized automaton (502), which is the result ofdeterminizing a particular input automaton such as the automaton 100shown in FIG. 1. The initial state is given a label of 0′. This initialstate is shown on FIG. 2 as state 0′. Next, a state queue pair isinitialized (504). Initializing a state pair includes the creation of afirst queue pair (0′,0) that comprises a state variable that correspondsto the state 0′ and an initial cost element of 0. Initialization alsosets all of the counters r[p] to 0, where r[p] represents the number oftimes a particular state has been extracted from the queue.

Next the initial state queue pair created above is placed in a queue S(506). The results of placing the initial state queue pair into thequeue are shown in FIG. 6 at a time shown in row 601. At time 1, thecontents of the queue are the queue pair (0′,0). The pairs or subsetsthat correspond to a particular state are identified as previouslydescribed.

Then the process 500 checks the status of the queue (508). If the queueis empty, the process 500 ends (510). Because the initial queue pair(0,0) has been placed in the queue, the queue is not empty and theprocess 500 prioritizes the queue (512).

The process 500 then selects the element from the queue with the highestpriority (514). At this point in the process the selected pair is(0′,0). A pair counter function r[p] associated with state 0′ (the firstnumber in the state pair extracted from the queue) is incremented (516).This function r[p] had a value of 0 prior to being incremented, and hasa value of 1 after being incremented. However, because state 0 is not afinal state, this counter will not indicate how many times a path hasreached a final state and is therefore uninteresting for this example.The value of r[p] for the final state is compared to the value N todetermine if the N-best paths for the determinized automaton have beenrealized (518). Because state 0 is not a final state, the process takesthe “no” path at 518.

The process 500 then calculates the cost elements of new queue pairsthat will be created and added to the queue (520). New cost elementsmust be calculated for each transition leaving state 0′ of thedeterminized automaton 200. Referring to the input automaton 100, thereare two transition labels associated with all of the transitions leavingthe initial state 0, namely a and b.

At this point, because it is known that the destination states thattransitions a and b will reach in the determinized automaton 200 areneeded, they can be created on the determinized automaton 200. A newstate labeled 1′ is created. As noted above, the states in thedeterminized automaton comprise weighted subsets {(q_(o), w_(o)), . . ., (q_(n,) w_(n))} where each q_(i)εQ is a state of the input machine,and w_(i) a remainder weight.

A new transition from state 0′ to state 1′ is created according to therules set forth above. In the present example, referring to FIG. 1, thetransition a leaving state 0 has a weight of 0.1 to destination state 1,and weights of 0.2 and 0.4 to destination state 2. Therefore, the weightof the new transition a formed on the determinized automaton 200 is 0.1.This is true because the remainder weight w_(i) for the state 0 wasdefined to be 0 and the smallest weight of the transition w[e] (theweight of the transition to state 1) is 0.1. Note that there are twodestination states that transition a could reach in the input automaton,namely 1 and 2. The transition to the newly created transition islabeled a and given a weight of 0.1 as shown by the transition 201 inFIG. 2. Once the weight of the transition a is known, the weight (w′) ofthe weighted subsets that comprise the label of the new state 1′ can becalculated. Because there were two paths for the transition a to reach asubsequent state in the input automaton, the new state 1′ will have twoweighted subsets or pairs. The first weighted subset or pair is (1,0).The first number 1 corresponds to state 1 in the input automaton whichwas a destination state for the transition a. The second number iscalculated by using equation (5) above.

Note however, that there is a second path that transition a could take,namely to state 2 of the input automaton 100. Therefore, a weightedsubset of state 1′ corresponding to this possible path needs to becreated. This weighted subset is (2,0.1). The first number 2 correspondsto the state 2 of the input automaton 100. The second number 0.1 is theweight calculated from equation (5) above.

A similar process is performed for creating transition b to destinationstate 2′ on the determinized automaton 200. Note that using the aboveprocess, state 2′ has weighted subsets of (2,0) and (1,0.2).

For each of the newly created states, namely 1′ and 2′, on thedeterminized automaton, the cost elements for the queue pairs need to becalculated (520). The cost element is dependent on the potential of eachof the new states in the determinized automaton. The determinizedpotential of each state q′ is calculated using equation (8) above. Thispotential represents the shortest path from the current state to thefinal state in the determinized automaton 200. The determinizedpotential can be calculated before any final state has actually beencreated.

The determinized potential for state 1′ is 0.2. This is calculated byusing the weighted subsets (q₁, w₁) (1,0) and (q₂,w₂) (2,0.1). Fromabove, it is known that the potential of state 1 in the input automaton100 is 0.2, and the potential of state 2 is 0.2. By equation (8) thepotential of state 1′ is 0.2. Similarly, the potential for the state 2′is 0.2.

After the potentials have been calculated, the cost elements for newqueue pairs can be calculated (520). Calculating cost elements (520) isnecessary for creating new pairs that will be inserted into queue S. Anew pair must be calculated for every outgoing transition of thedeterminized automaton 200. In this example, because the first pair fromthe queue (0′,0) is used corresponding to state 0′ of the determinizedautomaton, there are two outgoing transitions, namely a and b. The costelement is the sum of the current cost element plus the weight of thetransition leaving the current state. In the current example, thisresults in two new cost elements, 0+0.1=0.1 for the transition a tostate 1′ and 0+0.1=0.1 for the transition b to state 2′.

The N-best string process 500 assigns the newly created states, namely1′ and 2′, to new queue pairs (522). New queue pairs are created wherethe first number is a state element that represents a destination statefrom the state represented by the preceding queue pair previously poppedfrom the queue, and the second number represents the cost calculatedabove (520). For this example, the new pairs that are created are(1′,0.1) and (2′,0.1) where 1′ represents the destination state oftransition a from state 0′, 0.1 represents the cost of that transition,2′ represents the destination state of transition b from state 0′, and0.1 represents the cost of that transition.

The newly created queue pairs are made to conform to the queue formatand placed in the queue (524). At this point the modified N-best stringsprocess 500 returns to check the status of the queue (508) and becausethe queue is not empty, the queue is prioritized (512).

Prioritization (512) orders all of the elements in the queue so thatbased on the queue's ordering, a particular pair will be popped from thequeue when the process gets a queue pair from the queue (514). Priorityis assigned to each element in the queue according to equation (9).

This equation implies that any pair in the queue whose cost element plusthe potential of the state the pair represents is less than any otherpair's cost element plus the potential of the state that pair representsis given a higher priority. Using this ordering, the contents of thequeue are arranged at this point in our example as shown at a time 2shown in row 602 of FIG. 6. Note that in this example, the pairs in thequeue both have an ordering variable that is equal. In this case, thequeue can randomly select either pair. In our example, the pair (1′,0.1)has arbitrarily been given higher priority.

The top queue pair is then selected from the queue (514) which is(1′,0.1). Again because this pair is not a final state, the N-beststrings process 500 flows uninterestingly to a point where the costelements for subsequent states need to be calculated (520). Because atthis point states subsequent to state 1′ are needed on the determinizedautomaton 200, any states to which transitions from state 1′ will floware constructed.

First, a new state 3′ is created. Transitions from state 1′ to the newlycreated state 3′ are created. In the input automaton 100, thetransitions 102 that could be taken after transition a are transitions cand d. Thus, a transition c is created from state 1′ to 3′. The weightof this transitions is given by equation (4) above.

For the weighted subset of 1′ (1,0), the remainder weight is 0 and thetransition weight for path c is 0.5, therefore, w_(i)+w[e]=0.6. For theweighted subset of 1′ (2,0.1), the remainder weight is 0.1 and theweight of the transition for path c is 0.3, therefore w_(i)+w[e]=0.4.The minimum of the two above is of course 0.4. Therefore, the transitionc from 1′ to 3′ is 0.4. Using a similar analysis, the weight of thetransition d from state 1′ to state 3′ is 0.4.

Next, weighted subsets for the new state 3′ are created. The weightedsubset associated with state 3′ for path c is (3,0), where 3 is thedestination state in the input automaton 100, and 0 is calculated usingequation 5 above. Note that because the first element is 3, and 3 was afinal state in the input automaton 100, the state 3′ is a final state inthe determinized automaton 200. The process for path d is similar to theone for c and yields a weighted subset state pair of (3,0). Thepotential of the new state 3′ is then calculated. The potential forstate 3′ is 0 using the equations for potential above.

The cost elements for all transitions leaving the current state, namely1′, are calculated (520). Using the method described above, the cost forthe queue pair representing transition c from state 1′ is 0.5.Similarly, the cost element for transition d leaving state 1′ is 0.3.New state 3′ is then assigned to new queue pairs (522); namely, thequeue pairs (3′,0.5) and (3′,0.3) are created for the transitions c andd respectively from state 1′ to 3′. The new queue pairs are thenvalidated and added to the queue S.

The process 500 then returns to check the status of the queue (508) andcontinues as described above until the N-best paths on the new automaton(or the result of determinization) have been extracted. Note that bylooking at the queue at a time 3 shown in row 603 in FIG. 6, the nextqueue pair to be popped from the queue is a final state pair because 3′is a final state. Therefore, the r[p] variable associated with thisstate is important because it tells us that a final state has beenreached one time. If only the 1 (N=1) best path is needed, it has beenfound at this point and the modified N-best strings process 500 couldend (510). If more than the one best path is desired, then the processwould continue until more queue pairs representing the final state hadbeen extracted. Examining the queue in FIG. 6, it can be observed thatat the times shown in rows 605, 606, and 607 final states will be poppedoff of the queue. If the two best paths are needed, the process 500 canbe ended after time 5 in row 605. If the three (N=3) best paths areneeded, the process 500 can end after a time 6 in row 606, and so forth.Note also that after a time 8 shown in row 608, the process will endwhen the queue status is checked (508) because the queue is empty.

It should be noted that the above example is just one example of oneN-best paths process that may be used. Other N-best paths processes thatdepend on the value of the potential of a given state may also be usedto implement the on-the-fly determinization described above.

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the invention is, therefore, indicatedby the appended claims rather than by the foregoing description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

What is claimed is:
 1. A method for finding N-best distinct hypothesesof an input automaton, the method comprising: computing, via a speechrecognition system, an input potential for each state of a plurality ofstates of the input automaton to a set of final states, wherein theinput potential of each state is used to determine a determinizedpotential of the state in a result of determinization of the inputautomaton and wherein the determinized potential of a particular statein the result of determinization is determined without fullydeterminizing the input automaton; removing redundant paths; andidentifying N-best distinct paths in the result of determinization ofthe input automaton using the determinized potential of each of thestates in the result of determinization, wherein the N-best distinctpaths in the result of determinization comprise more than one best pathand are labeled with the N-best hypotheses of the input automaton,wherein the identifying the N-best distinct paths comprises: adding aninitial state to the result of determinization of the input automaton;creating an initialized first queue pair comprising the initial stateand an initial cost element; placing the first queue pair in a queue;creating a plurality of new states from the first queue pair; applying ashortest path algorithm to each of the new states to calculate ashortest path of each of the new states; creating new queue pairs usingthe new states and cost elements of each new queue pair calculated viathe shortest path algorithm; adding the new queue pairs to the queue;prioritizing the queue based upon a cost element of each queue pairrelative to each other queue pair in the queue, wherein a queue pair inthe queue with a lower cost element is given a higher priority thananother queue pair in the queue with a higher cost element; selecting aqueue pair from the queue with a highest priority; incrementing a paircounter; and determining whether a value of the pair counter is equal toa desired number of best paths.
 2. The method of claim 1, wherein thecomputing the input potential for each state of the input automaton tothe set of final states further comprises running a shortest-pathsalgorithm from the set of final states using a reverse of a digraph. 3.The method of claim 1, wherein the identifying N-best distinct paths inthe result of determinization of the input automaton further comprisescomputing the result of determinization on-the-fly.
 4. The method ofclaim 3, wherein the computing the result of determinization furthercomprises: creating a new state in the result of determinization;creating a new transition from a previous state to the new state in theresult of determinization, wherein the new transition has a label thatis the same as a label from a transition of the input automaton;creating a subset of state pairs that correspond to the new state; anddetermining a determinized potential for the new state using an inputpotential from a state of the input automaton.
 5. The method of claim 4,wherein each state pair in the subset of state pairs includes a statefrom the input automaton and a remainder weight, wherein the creatingthe subset of state pairs further comprises constructing a state pairfor each destination state of the transition in of the input automaton,wherein each state pair for each destination state of the transition ofthe input automaton includes a state of the input automaton and aremainder weight.
 6. The method of claim 4, wherein the creating the newtransition from the previous state to the new state in the result ofdeterminization only depends on states and remainder weights of aparticular subset corresponding to the previous state in the result ofdeterminization and on the input automaton.
 7. The method of claim 1,wherein the identifying N-best distinct paths in the result ofdeterminization of the input automaton using the determinized potentialof each of the states in the result of determinization further comprisespropagating the input potential of a particular state to states in theresult of determinization.
 8. A method for identifying the N-bestdistinct strings of an automaton, the method comprising: partiallydeterminizing, via a speech recognition system, the automaton during asearch for the N-best distinct strings, wherein the N-best distinctstrings comprise more than one best distinct string, by creating apartially determinized automaton while searching for the N-best distinctstrings by: creating an initial state of in the partially determinizedautomaton, wherein the initial state corresponds to a state pair;creating a transition leaving the initial state, wherein the transitionhas a label and a weight; creating a destination state for thattransition, wherein the destination state corresponds to a subset ofstate pairs; creating additional states in the partially determinizedautomaton, wherein each additional state corresponds to a differentsubset of state pairs and wherein the additional states in the partiallydeterminized automaton are connected by transitions that have labels andweights; and propagating a potential from a state of the automaton toeach state in the partially determinized automaton; removing redundantpaths; and identifying the N-best distinct strings of the automaton fromthe partially determinized automaton using an N-best paths process,wherein the identifying the N-best paths comprises: adding an initialstate to the partially determinized automaton; creating an initializedfirst queue pair comprising the initial state and an initial costelement; placing the first queue pair in a queue; creating a pluralityof new states from the first queue pair; applying a shortest pathalgorithm to each of the new states to calculate a shortest path of eachof the new states; creating new queue pairs using the new states andcost elements of each new queue pair calculated via the shortest pathalgorithm; adding the new queue pairs to the queue; prioritizing thequeue based upon a cost element of each queue pair relative to eachother queue pair in the queue, wherein element a queue pair in the queuewith a lower cost element is given a higher priority than a queue pairin the queue with a higher cost element; selecting a queue pair from thequeue with a highest priority; incrementing a pair counter; anddetermining whether a value of the pair counter is equal to a desirednumber of best paths.
 9. The method of claim 8, further comprisingcomputing an input potential for each state of the automaton, whereineach input potential represents a shortest distance from a correspondingstate to a set of final states.
 10. The method of claim 9, wherein thecomputing the input potential for each state of the automaton furthercomprises running a shortest-paths algorithm from the set of finalstates using a reverse of a digraph.
 11. The method of claim 8, whereinthe identifying the N-best distinct strings of the automaton from thepartially determinized automaton occurs without fully determinizing theautomaton.
 12. The method of claim 8, wherein the creating additionalstates in the partially determinized automaton further comprisescreating new transitions that connect previous states in the partiallydeterminized automaton with the additional states, wherein the creatingthe new transitions depends on the different subset of state pairs andthe automaton, wherein each state pair in the different subset of statepairs includes a state of the automaton and a remainder weight.
 13. Themethod of claim 8, wherein the partially determinizing the automatonduring the search for the N-best distinct strings comprisesdeterminizing only a portion of the automaton visited during the searchfor the N-best strings.
 14. The method of claim 8, wherein the partiallydeterminizing the automaton during a search for the N-best distinctstrings further comprises: creating subsets of state pairs for eachstate of the partially determinized automaton, wherein each state pairin each of the subsets of state pairs includes a state of the automatonand a remainder weight; and assigning a weight to a final state of thepartially determinized automaton.
 15. The method of claim 8, furthercomprising terminating the search for the N-best strings when a finalstate of the result of determinization has been extracted N times. 16.The method of claim 8, further comprising prioritizing state pairs ineach of the subsets of state pairs according to a determinizedpotential.
 17. A method of partially determinizing an input weightedautomaton to identify the N-best strings of the input weighted automatonwhere the input weighted automaton comprises input states and inputtransitions, wherein the input transitions interconnect the input statesto form a plurality of complete paths from any one member of a set ofbeginning input states to any one member of a set of final input states,wherein each of the input transitions comprises a label and a weight,the method comprising: creating a deterministic automaton, via a speechrecognition system, by: forming determinized states and determinizedtransitions in an order dictated by an N-shortest paths algorithm tocreate N complete paths using only a part of the input weightedautomaton; and interconnecting the determinized states and determinizedtransitions to form complete paths; removing redundant paths; andidentifying the N-best strings of the input weighted automaton bysearching for the N-best complete paths of the deterministic automaton,wherein the N-best complete paths comprise more than one best completepath, wherein the identifying the N-best strings comprises: adding aninitial state to the deterministic automaton; creating an initializedfirst queue pair comprising the initial state and an initial costelement; placing the first queue pair in a queue; creating a pluralityof new states from the first queue pair; applying a shortest pathalgorithm to each of the new states to calculate a shortest path of eachof the new states; creating new queue pairs using the new states andcost elements of each new queue pair calculated via the shortest pathalgorithm; adding the new queue pairs to the queue; prioritizing thequeue based upon a cost element of each queue pair relative to eachother queue pair in the queue, wherein a queue pair in the queue with alower cost element is given a higher priority than a queue pair in thequeue with a higher cost element; selecting a queue pair from the queuewith a highest priority; incrementing a pair counter; and determiningwhether a value of the pair counter is equal to a desired number of bestpaths.
 18. The method of claim 17, wherein the deterministic automatonrepresents a word lattice.
 19. The method of claim 17, wherein each ofthe determinized transitions has a weight that corresponds to aprobability.
 20. The method of claim 17, further comprising computingpotentials for each of the input states of the input weighted automatonprior to the creating.